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Proceedings of the American Mathematical Society

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A univalent function nowhere semiconformal on the unit circle


Author: Shinji Yamashita
Journal: Proc. Amer. Math. Soc. 69 (1978), 85-86
MSC: Primary 30A36; Secondary 30A30
DOI: https://doi.org/10.1090/S0002-9939-1978-0466525-6
MathSciNet review: 0466525
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Abstract: We shall construct a function f holomorphic and univalent in the open unit disk such that f is not semiconformal at any point of the unit circle. It is also shown that f may be extended quasiconformally to the whole extended plane.


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  • [1] J. Becker, Löwnersche Differentialgleichung und quaikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23-43. MR 0299780 (45:8828)
  • [2] D. M. Campbell and J. A. Pfaltzgraff, Boundary behaviour and linear invariant families, J. Analyse Math. 29 (1976), 67-92. MR 0477054 (57:16598)
  • [3] P. Lappan, Fatou points of harmonic normal functions and uniformly normal functions, Math. Z. 102 (1967), 110-114. MR 0222265 (36:5317)
  • [4] C. Pommerenke, Linear-invariante Familien analytischer Funktionen. II, Math. Ann. 156 (1964), 226-262. MR 0168751 (29:6007)
  • [5] -, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, vol. 25, Vandenhoeck und Ruprecht, Göttingen, 1975. MR 0507768 (58:22526)
  • [6] C. Visser, Über beschränkte analytische Funktionen und die Randverhältnisse bei konformen Abbildungen, Math. Ann. 107 (1933), 28-39. MR 1512784
  • [7] J. L. Walsh and D. Gaier, Zur Methode der variablen Gebiete bei der Randverzerrung, Arch. Math. 6 (1955), 77-86. MR 0064874 (16:348c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0466525-6
Article copyright: © Copyright 1978 American Mathematical Society

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